Sphere shaped structure



Sept. 23, 1969 HADLEY 3,468,082

SPHERE SHAPED STRUCTURE Filed July 19, 1966 3 Sheets-Sheet 1 LE.ZI.

INVENTOD EMEQSON E. HADLEY Wigs.

P 23, 1969 E. E. HADLEY 3,468,082

Filed July 19. 1966 3 Sheets-Sheet P Sept. 23, 1969 E. E. HADLEY SPHERE SHAPED STRUCTURE 3 Sheets-Sheet 5 Filed July 19. 1966 U.S.- Cl. 52-81 1 Claim ABSTRACT on THE DISCLOSURE Spheres and sphere shaped structures are constructed by utilizing, as the main structural members, fiat frame members which may be stamped or cut from sheets of material such as metal, wood, fiberglass or plastic. These flat frame structural members are arranged to form spherical regular polyhedrons.

The present invention relates to spheres and sphere shaped structures.

In the past building structures had been composed of structural members forming regular polyhedrons in geometric shape. Attempts have been made to extend the edges of such regular polyhedrons as regular icosahedrons and regular dodecahedrons to define a spherical surface which intersects the vertices of the polyhedron being utilized. The resulting structures have not usually been true spheres, being only approximations thereof; or where true spheres have been obtained, they have been obtained only with relatively complicated structure. The present invention provides a simple and economical framework for constructing true sphere shaped structures. The present invention makes it possible to construct sphere shaped structures utilizing, as the main structural members, fiat frame members which may be stamped or cut from sheets of material such as metal, wood, fiberglass or plastic. Further, the present invention makes it possible to construct such structures of flat'sheet frame members wherein only one or two sizes of members are required throughout the finished building structure.

Thus, it is an object of the present invention to provide new and improved sphere shaped structures.

Further objects and advantages will become apparent from the following detailed description taken in connection with the accompanying drawings, in which:

FIGURE 1 is a regular icosahedron having twenty equal sides formed by equilateral triangles;

FIGURE 2 is a regular dodecahedron having twelve equal sides formed by regular pentagons;

FIGURE 3 is a perspective view of a spherical regular icosahedron;

FIGURE 4 is a perspective view of a spherical regular dodecahedron;

FIGURE 5 is a perspective view of a preferred embodiment of myinvention constructed by subdividing a spherical regular icosahedron; and

FIGURE 6 is a modification of the embodiment of my invention illustrated in FIGURE 5 utilizing a spherical regular dodecahedron.

3,468,082 Patented Sept. 23, 1969 While this invention is susceptible of embodiment in many different forms, there is shown in the drawings and will herein be described in detail embodiments of the invention with the understanding that the present disclosures are to be considered as exemplifications of the principles of the invention and are not intended to limit the invention to the embodiments illustrated. The scope of the invention will be pointed out in the appended claim.

FIGURE 1 illustrates the basic geometrical figure of a regular icosahedron. For the purposes of describing the structure of the embodiment of my invention illustrated in FIGURE 5,'vertices 10, 11 and 12 of one equilateral triangle of the twenty equilateral triangles forming the twenty faces of the regular icosahedron illustrated in FIGURE 1 will be described in detail, since the structures of the other nineteen triangles are identical. If each edge formed between the vertices of the icosahedron illustrated in FIGURE 1 is extended outwardly in a plane that passes'through the geometric center of the icosahedron to a spherical surface formed by a sphere passing through all the vertices of the icosahedron illustrated in FIGURE 1, then a sphere 20, as illustrated in FIGURE 3, is created wherein each of the equilateral triangles of the icosahedron shown in FIGURE 1 is extended to form a spherical regular triangle on the surface of the sphere 20. The numerals indicating the vertices 10, 11 and 12 in FIGURE 3 are joined by great circle arcs on the surface of the sphere to form a spherical equilateral triangle. The

midpoints of the .arcs forming the spherical triangle 10-11-12 are midpoints 21, 22 and 23, respectively. If these arcs are joined by great circles on the surface of the sphere, a spherical equilateral triangle A and three spherical isosceles triangles B, C and D are formed as indicated in FIGURE 3.

Triangle A is an equilateral triangle while the triangles B, C and D are isosceles spherical triangles. The spherical triangle formed by a vertex 24 and vertices 11 and 12 is also shown subdivided at its midpoints 22, 25 and 26, to subdivide the triangle 11-24-12 into four spherical triangles in the same manner as triangle 10-11-12 is divided. At each of the vertices 10, 11 and 12 and 24, five spherical arcs defining the spherical triangles are joined together, while at a midpoint vertex such as 22,

where the triangles are divided, six spherical arcs are joined together. This provides a total of twenty equilateral triangles and 'sixty isosceles triangles. The arcs formed on the face of a sphere such as 20 (when the twenty faces of a spherical regular icosahedron is divided by drawing arcs through the midpoints of each side of the equilateral triangles making up the spherical icosahedron) are composed of two different length arcs between the vertices so formed. One length of arc is that required to form eachside of the twenty equilateral triangles which are formed between the midpoints of the original arcs of the spherical icosahedron. A slightly shorter are forms the equal sides of the sixty isosceles spherical triangles which have one vertex at the vertices of the original icosahedron.

Referring now to FIGURE 5, a sphere shaped structure or framework is illustrated wherein all of the members which form the structural beams of the structure have their outer and inner edges shaped in the form of arcs of great circles of an outer and an inner sphere. The vertex points of the spherical equilateral triangles 1t), 11 and 12 are indicated by the same numerals in FIGURE 5 as they were in FIGURES l and 3. In like manner, the vertex of the subdividing triangle 21-22-23 shown in FIGURE 3 is marked by corresponding numerals in FIGURE. 5. A structural length of beam is provided between the points 10-11, 11-12 and 12-10 by pairs of flat beam members 30-31,

32-33 and 34-35. Since each one of the members -35 are of equal length and size, only beam member 30 will be described in detail. The beam member 30 is a fiat frame member which may be of any material such as wood, plywood, metal, plastic, or fiberglass. Both its outer edge and its inner edge form an arc of a predetermined radius which are the respective radii of an outer and an inner sphere defined by the outer and inner edges of all the frame members forming the structure. A slot 37 is provided in one end, and a slot 38 is provided in the other end thereof. A disc 40 and a disc 41 have respective slots 42 and 43 which cooperatively fit into the slots 37 and 38, respectively, as illustrated in FIGURE 5. The respective slots 37-42 and 38-43 cooperatively join the frame member 30 with the discs 40 and 41, respectively, until the ends of the frame member 30 are in contact with rods or dowels 44 and 45, respectively.

A set of three frame members 90-92 join the vertex points 21-22-23 to form the subdividing spherical triangle which subdivides the spherical triangle 10, 11 and 12. These frame members are slightly longer than frame members 30-35. They are secured to the respective rods as dowels 93, 45 and 95 by the use of respective discs 94, 41 and 96 by fitting respective slots together, as previously described, and gluing or otherwise securing the frame members, disc and rods in the positions illustrated in FIG- URE 5. Therefore, the entire sphere structure shown in FIGURE 5 comprises only two sizes of frame members, two different sizes of connecting discs (one with five slots and one with six slots), and dowel or rod sections approximately equal in length to the radial width of the frame members. Both the frame members and discs can be easily cut or stamped out of sheet material regardless of the material desired to be used for the construction. This makes the structure relatively inexpensive over structures pre- 1 viously utilized, since it lends itself particularly well to mass production of a large number of only five different simple parts.

By referring to FIGURES 2. 4 and 6, a modification of my invention of that illustrated by the discussion of FIG- URI-TS 1, 3 and 5 will now be described. FIGURE 2 illustrates a regular dodecahedron which is comprised of twelve faces formed by regular pentagons such as the pentagon having vertices 50, 51, 52, 53 and 54. When the sides of the regular dodecahedron shown in FIGURE 2 are extended to form a sphere as illustrated in FIGURE 4, the vertices -54, which are indicated in FIGURE 4 by the same numerals, form a spherical pentagon as illustrated in FIGURE 4. If the spherical polygon 50-51-52-53-54 of FIGURE 4 is divided into five triangles with a new vertex 55 formed thereby-laying on the surface of a sphere formed by the vertices of the dodecahedron illustrated in FIGURE 2, then five new spherical isosceles triangles are formed.

In constructing the sphere shaped structure in accordance with my invention illustrated in FIGURE 6, all of the twelve faces of the spherical dodecahedron as illustrated in FIGURE 4 are divided into five isosceles spherical triangles to thereby form a total of sixty isosceles triangles. The vertices 50-55 illustrated in FIGURE 4 are utilized in FIGURE 6 and bear the same numerals. The spherical subdivided polygon 50-51-52-53-54 is defined'as illustrated in FIGURE 6 by ten fiat frame memhers 70-79. Since all sixty of these triangles are isosceles triangles, the frame members 70-74 will be of one equal length and the frame members 75-79 will be of another equal length. These frame members are otherwise similar to the frame members illustrated in FIGURE 5 having their outer edges equal to a predetermined radius of a preselected sphere and their inner edges defining an are having a radius equal to another preselected sphere. The members connecting at the original vertex points 50-54 are joined by discs, such as disc 80, which has six slots in it and a dowel or rod 8|, and the members joining at the new vertices such as 55 are joined by a disc such as 82 having five slots therein and a dowel or rod such as 83. Thus, only two sizes of fiat members are required for the frame members of the sphere shaped structure illustrated in FIG- URE 6, and only two types of discs (five and six slot discs) together with one size of dowel or red are required. Therefore, the sphere shaped structures illustrated in FIGURES 5 and 6 may each be constructed of only three types of parts, two of which are required in only two different sizes or shapes, and the other required in only one size. For purposes of keeping FIGURE 6 simplified, only one of the spherical polygons is shown subdivided into isosceles triangles. The remaining eleven pentagons may be similarly divided.

With the size of structure that makes it desirable only to use the basic twelve sided spherical regular dodecahedron, the subdividing illustrated in FIGURE 6 may be eliminated. Then only three types of parts will be required in the building of the structure framework (one size of fiat frame member, one type of five slotted disc and one type of rod). In like manner, the subdivision illustrated in FIGURE 5 of the twenty equilateral faces of the original icosahedron could be eliminated, and then only three types of parts would be required in such a structure. Similarly, if it is desired to make an extremely large structure, the isosceles and equilateral triangles defined by these structures illustrated in FIGURES 5 and 6 may be further subdivided at their midpoints as described for the original divisions of the equilateral triangles in the icosahedron and the regular pentagons in the dodecahedron. Still only a very few types of parts would be required for the construction even for a framework that is so formed from many subdivisions of the respective resulting spherical triangles.

Covering the frameworks'illu'strated in FIGURES 5 and 6 with approximately shaped panels or coverings sections provides the spheres illustrated in FIGURES 3 and 4, respectively. Such covering material can be easily applied to either the inner edges or the outer edges of the frameworks in any approximate manner known to those skilled in the art, since these edges are great circle arcs of predetermined sphere sizes.

Other regular polyhedrons can be utilized as a basis for providing a sphere shaped structure in accordance with my invention. For example, the simplest polyhedron that can be extended to a spherical polyhedron would be a square extended to form a sphere surface having spherical squares on the surface thereof. Thus, my invention is intended to be applied to the geometrical shape which is created by taking any regular polyhedrons and extending it into a spherical regular polyhedron and then providing frame members having either external or internal edges defining-great circle arcs of a sphere of a desired radius. It is also part of my invention to subdivide the sides of any such polyhedron in order to make the structural frame members of a feasible size for large structures. The scope of the appended claims is intended to include all such modifications.

Since the twenty spherical surfaces which are defined by the frame members making up the original spherical icosahedron of FIGURE 5 and the twelve spherical surfaces which are defined by the frame members composing the original dodecahedron of FIGURE 6 are in equal size surfaces. panels or covering sections may be prepared which-are all identical to either cover the inside or the outside of the frame structure illustrated in either FIGURE 5 or FIGURE 6. To cover both the inside and the outside of the sphere shaped structure shown in these figures, only two sizes of covering sections would be required. If the respective icosahedron and dodecahedron illustrated in FIGURES 5 and 6 are subdivided as illustrated therein, and if it were desirable to cover each resulting triangle with a separate section, then only two different shapes of sections would be required to cover the outer surface and two different shapes of sections would be required to cover the inner surface.

6 A sphere formed by either covering the outer surfaces means for connecting the ends of said members at a or the inner surfaces can have many uses. It can be used multiplicity of intersections to form a spherical reguas a building structure, either as a complete sphere or as a lar polyhedron, said means being comprised of a partial sphere, by cutting off the spherical structure at rod at each intersection of said fiat frame members appropriate points and joining it to other structure. It may 5 against which said ends of the flat frame members be used in my movable spherical mounting structure disabut, a slot in each said end of the flat frame memclosed in my copending application. It may be used as bers, and a disc at each intersection of said flat frame a sizeable fluid storage tank. It is particularly adaptable as members surrounding said rod at each respective ina floating structure, either in a small or a large size. Furtersection and being received in said slots of said ther, my invention can be utilized to construct diving 10 ends forming each respective intersection, and bells for underwater exploration. covering sections of material secured to the arc defining What is claimed: surfaces of said members. 1. A sphere shaped structure comprising: a multiplicity of flat frame members, each said member References Cited being void of projections therefrom, UNITED STATES PATENTS 31 .2%.ififfiffi iaiffi 252132Li23; 52-81 unit and a center reference plane parallel to said 2978O74 4/1961 schmldt 52-81 long sides, each of said center reference planes 3114176 12/1963 Mluer 52-81 1533i, m a plane wh1ch intersects a common FRANK L. ABBOTT, Primary Examiner having an outer surface, defined by one of said SAM D. BURKE III, Assistant Examiner short sides of said rectangular cross section, that defines an arc of a predetermined radius from US- 1- X-R. said common point, and 52648 having ends, 

